How do you find the derivative of #f(x)=5sqrtx#?

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Answer 1 · 2016-05-11T18:01:28

#f'(x)=5/(2sqrt(x))#

Given,

#f(x)=5sqrt(x)#

Rewrite the expression using #(dy)/(dx)# notation.

#d/(dx)(5sqrt(x))#

Using the multiplication by a constant rule, #(c*f)'=c*f'#, bring out the #5#.

#=5*d/(dx)(sqrt(x))#

Rewrite #sqrt(x)# using exponents.

#=5*d/(dx)(x^(1/2))#

Using the power rule, #d/(dx)(x^n)=n*x^(n-1)#, the expression becomes,

#=5*1/2x^(1/2-1)#

Simplify.

#=5*1/2x^(-1/2)#

#=5/2(1/x)^(1/2)#

#=5/2((1)/(sqrt(x)))#

#=color(green)(|bar(ul(color(white)(a/a)color(black)(5/(2sqrt(x)))color(white)(a/a)|)))#